Unleashing the Power of Machine Learning: Efficient Detection of Tunneling Defects in Glass Models

By Dr. Sampath LonkaReviewed by Susha Cheriyedath, M.Sc.Jul 18 2023

In a paper published in the journal Nature Communications, researchers employed a machine learning (ML) approach to explore the potential energy landscape of glass models and detect structural defects.

Background

When a liquid cools rapidly, its viscosity increases, leading to the formation of glass, an amorphous solid with distinct properties from crystalline solids. At extremely low temperatures, the specific heat of a disordered solid is significantly higher than that of its crystalline counterpart, scaling linearly with temperature instead of cubically. The thermal conductivity in glasses follows a quadratic temperature evolution rather than a cubic one. Anderson, Halperin, Varma, and Phillips proposed a theoretical framework explaining these anomalies, emphasizing the presence of TLS as tunneling defects within the energy landscape of amorphous solids.

New developments in particle-swap computer algorithms and potential energy landscape exploration have allowed researchers to create and study computer glasses at extremely low temperatures. This advancement made it possible to directly observe TLS through numerical simulations. These studies confirm the depletion of tunneling defects as glass stability increases. ML techniques have proven valuable in predicting defects, and in the current study, the researchers demonstrate their relevance in identifying TLS.

Methods

The study focuses on a three-dimensional polydisperse mixture of 1500 particles with equal mass. The particle diameters are drawn from a normalized distribution. A repulsive pair potential governs the interaction between particles. The energy and length units are defined, and times are expressed in units of molecular dynamics (MD) simulations. Glass samples are prepared by equilibrating liquid configurations at different temperatures using a hybrid MD or particle-swap Monte Carlo algorithm. The energy landscape is explored using classical MD simulations, and the transition matrix is computed to analyze the dynamics of IS. The ML approach involves constructing input features for pairs of IS and using model ensembling and gradient boosting for DW classification and QS prediction. The iterative training procedure is introduced to enhance the ML model's performance by iteratively retraining it on new data. Computational times for each step of the ML procedure are reported, along with the estimated total computational time for processing a given number of IS pairs.

Results

The study's main focus was on detecting rare tunneling TLS. The researchers effectively used their ML approach to predict classical energy barriers between energy minima, resulting in the efficient detection of different types of defects.

ML approach: The standard procedure for identifying TLS involves several steps. Equilibrating the system at the preparation temperature is followed by molecular dynamics simulations of sample configurations. Energy minimization produces a time series of inherent structures (IS). Transitions between pairs of IS are analyzed, and consecutively explored pairs are selected for further investigation. However, only a subset of pairs can be analyzed due to computational limitations. This procedure is time-consuming and often results in wasted effort.

To address these limitations, the researchers introduced an ML approach based on supervised learning. It requires a dataset of NEB calculations and takes a few hours to train. Once trained, the ML model can predict TLS more efficiently. The workflow involves obtaining IS, applying the ML model to predict double well (DW) potentials, filtering based on the predicted quantum splitting (QS), and running NEB calculations for the predicted TLS pairs. The ML model considers all pairs of IS as TLS candidates and improves the detection process by significantly reducing computational time and increasing the number of identified TLS.

The well-trained ML model offers two advantages: scanning a larger number of pairs compared to the standard procedure and higher confidence in identified TLS. This approach allows for more time spent on producing new IS and enables the identification of a greater number of TLS.

Quality of the ML prediction: Previous studies analyzed libraries of IS for a continuous polydisperse system at different reduced temperatures. The standard approach identified a limited number of tunneling TLS using dynamical information and transition matrices. In contrast, the proposed ML approach considers all pairs of IS and accurately predicts the formation of DW potentials and the quantum splitting (QS) of TLS. The ML approach significantly increases the number of TLS candidates and achieves a good correlation between true and predicted QS values. The ML model is trained to classify DW and predict QS, and its performance can be extended to other types of state-to-state transitions, as demonstrated by predicting classical energy barriers.

ML expedited TLS search, generating an unprecedentedly large TLS library. Iterative training revealed insights into the TLS-dynamics relationship. ML-guided exploration led to ample TLS collection, enabling detailed analysis and comparison with DW. The proposed method identified 872 TLS in 11 iterations, surpassing prior efforts.

Microscopic features of TLS: The researchers demonstrated that filtering the number of recorded transitions between IS to identify DW and TLS is inefficient. Most TLS and DW pairs do not have recorded transitions, suggesting that the high-dimensional landscape prevents favorable transitions within a finite exploration time. Instead, the distribution of classical splitting and the largest particle displacement offer better indications. The ML model confirms these features' importance and suggests using a combination of the number of transitions and optimal values of classical splitting and displacements to quickly identify TLS.

Conclusion

In summary, the researchers proposed a supervised learning ML approach that not only boosts accuracy and expedites the process but also enables the identification of a substantial number of tunneling TLS defects. Moreover, they comprehensively explored the structural and dynamical characteristics of TLS and their evolution during glass preparation. Additionally, the methodology presented holds promise for addressing various other glass-related challenges, including supercooled liquid dynamics, plasticity, and devitrification.